I've never noticed this before but I've never seen anything like it. Two 40A brekers, I assume a separated double pole, for the range straddles the 30A dryer breaker? It's obviously designed this way since there's a bracket hooking the two switches together. Any idea why, or any cautions for me? Thanks in advance!
This is a quadplex breaker. Basically, in order to squeeze more stuff into breaker panels, many manufacturers came up with a way to squeeze two breakers into one space. The problem is that for 240V loads that doesn't work - you end up with 0V between the pair of breakers instead of 240V! So then they came up with quadplex - 4 breakers in 2 spaces. The inner 2 and the outer 2 are each 240V pairs, just like traditional double breakers.
I am not a breaker expert, but that looks to me like it may be "handle tie" rather than a true functional double breaker. Actually, the "All poles have no common trip" reinforces that the breakers are independent of each other, electrically speaking.
That is OK for some situations (MWBC), but if I am correct then that was never actually correct for a 240V circuit such as an oven. That being said, it doesn't matter if you are changing things anyway.
There are two possibilities here for your current (yes, pun intended) situation. You may be able to swap individual breakers, or you may have to deal with them as a set of 4 (quadplex). If they are individuals then you can pick one of the two 40A breakers and replace it with a 20A breaker. Based on the latest picture, the circuit is using neutral, so you can swap either breaker and leave the white neutral as-is. If the new gas range is hardwired, then you should be all set. If it has a plug and you are installing a 20A receptacle, you will likely need to pigtail the 8 AWG wires to 10 or 12 AWG wire to connect to the receptacle, as many can't handle 8 AWG wire.
Make sure the breakers are correct for the panel. There are a lot of similar breakers from different brands. The wrong ones might fit but won't fit correctly.
Also, in case it wasn't clear already, you can't replace a quadplex with two pairs of duplex breakers if even one of the pairs still needs 240V.
One fatal flaw in the existing setup is that the circuit breaker is labeled
All poles have no common trip
That makes them unfit to feed either a dryer or range -- both those loads are 240V loads with a neutral wire, and as such, they do require common trip. They would be acceptable for an air conditioner or water heater, which do not have neutral.
If you can find an appropriate 20-30-20 quadplex (which is to say: one with common trip in the middle), you could drop this in to replace the existing breaker, and change sockets and pigtail as needed to put your gas range on one of the 20's.